Traffic Density Modeling and Estimation on Stretched Highways: The Case for Lipschitz-Based Observers

摘要

As an alternative to installing traffic sensors on all highway segments, traffic density estimation routines can be utilized to estimate traffic state on sensor-less segments. To that end, we first derive a generalized traffic flow model for stretched highways with arbitrary number and location of ramp flows. The flow model is based on the Lighthill-Whitham-Richards (LWR) model and Greenshield's fundamental diagram. This derived model is written as a nonlinear state-space system, making it amenable to control-theoretic formulations for nonlinear dynamic networks. We then show that the nonlinearities present in the derived models are locally Lipschitz continuous by providing analytical Lipschitz constants that depend on the network parameters and topology. The analytical derivation is then used to perform traffic density estimation given a limited number of traffic sensors using a vintage Lipschitz-based state estimator. This estimator design graciously scales to thousands of highway segments. Numerical tests are given providing early confidence in the potential of the proposed methods.